Question

You want to buy a house that costs $1,609,009, but all you can afford to pay on a weekly mortgage for the house is $2,509.86 per week over 13 years. The bank quoted you are mortgage rate of 2.12%. How much can you actually afford to borrow?

Answer 1

Assuming 52 week in a years,

Affordable weekly payment A = $2509.86

Interest rate r = 2.12% APR compounded weekly

loan years = 13

since payment is weekly, so n = 52

Using ordinary annuity, PV of an annuity is

PV = A*(1 - (1+r/n)^(-n*t))/(r/n) = 2509.86*(1 - (1+0.0212/52)^(-52*13))/(0.0212/52) = $1482678.96

So, amount afford to borrow = $1482678.96